Prosser, 28, had two goals and eight points in 53 games for the Minnesota Wild last season. He was scoreless in 10 Stanley Cup Playoff games.
Prosser entered the NHL as an undrafted free agent and has three goals and 21 points in 126 regular-season games, all with the Wild.
The Blues also signed forward Jeremy Welsh to a one-year, two-way contract. Welsh had one goal in 19 regular-season games with the Vancouver Canucks last season, and 15 points (seven goals, eight assists) in 49 games with the Utica Comets of the American Hockey League. He has two points and 10 penalty minutes in 25 NHL games with the Canucks and Carolina Hurricanes, who signed him as a free agent in April 2012 after three seasons at Union College.